$ -\dfrac{3}{6} \div \left(\dfrac{1}{4} \div \dfrac{4}{3}\right) = {?} $
Explanation: First, we can simplify the problem: $ -\dfrac{1}{2} \div \left(\dfrac{1}{4} \div \dfrac{4}{3}\right) = {?} $ Dividing by a fraction is the same as multiply by the reciprocal of that fraction. $ = -\dfrac{1}{2} \div \left(\dfrac{1}{4} \times \dfrac{3}{4}\right) $ $ = -\dfrac{1}{2} \div \left(\dfrac{1 \times 3} {4 \times 4}\right) $ $ = -\dfrac{1}{2} \div \dfrac{3}{16} $ $ = -\dfrac{1}{2} \times \dfrac{16}{3} $ $ = \dfrac{-1 \times 16}{2 \times 3} $ $ = -\dfrac{16}{6}$ Simplify: $ = -\dfrac{8}{3}$